Equilibrium Moisture Transport
Assuming equilibrium, the total moisture content is defined by a sorption curve as
Summing Equation 4-142 and Equation 4-143, we obtain a single equation for the total moisture content, where the evaporation terms cancel each other out. The liquid and vapor sources are summed into a single source term G:
(4-144)
Under the equilibrium hypothesis, the source term is distributed between the liquid and vapor phases proportionally to the amount of liquid and vapor respectively, that is:
with the following material properties, fields, and source:
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w(ϕw) (SI unit: kg/m3) is the total moisture content.
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  ϕw (dimensionless) is the relative humidity.
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 ρg (SI unit: kg/m3) is the moist air density, defined from the dry air and vapor densities, in function of the amount of vapor.
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 ug (SI unit: m/s) is the moist air velocity field, that should be interpreted as the Darcy velocity, that is, the volume flow rate per unit cross-sectional area.
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 ωv (dimensionless) is the vapor mass fraction in moist air, defined as
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 Μv (SI unit: kg/mol) is the molar mass of water vapor.
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 csat (SI unit: mol/m3) is the vapor saturation concentration.
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 T (SI unit: K) is the temperature.
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 gw is the moisture diffusive flux is defined as:
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 Deff (SI unit: m2/s) is the effective vapor diffusion coefficient in the porous medium, computed from the diffusion coefficient in a free medium, and accounting for the porosity and tortuosity of the porous medium.
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 ul (SI unit: m/s) is the liquid water velocity field, defined from the absolute pressure gradient by the Darcy’s law as:
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 κrl (dimensionless) is the relative liquid water permeability, that may be defined as a function of the liquid saturation.
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 κ (SI unit: m2) is the porous medium permeability.
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 pA (SI unit: Pa) is the absolute pressure.
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 ρl (SI unit: kg/m3) is the liquid water density, defined as a function of the temperature.
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 glc is the liquid water capillary flux, defined either from the capillary pressure gradient by a Darcy’s law:
or by a diffusion equation using the relative humidity:
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 Dw (SI unit: m2/s) is the moisture diffusivity.
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 pc is the capillary pressure, that can be related to the relative humidity, in the scope of the equilibrium hypothesis, using Kelvin’s law:
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 G (SI unit: kg/(m3⋅s)) is a moisture source (or sink). See the Moisture Source node.
The moisture source due to evaporation can be obtained from Equation 4-143:
This moisture source is added as a mass source in the fluid flow equations solved for the computation of the moist air velocity field, ug.
The corresponding latent heat source is defined as:
where Lv is the latent heat of evaporation.
For a steady-state problem, the relative humidity does not change with time and the first term in the moisture transport equation disappears.